When DP sets a backup Permanent it will not overwrite the medium it was written to until you either expire the session manually or recycle the media.
When you run a Full on the 1st and a Full on the 15th they are completely separate backups. If you want to ensure they are on different tapes you will have to move the 1st jobs tape to another pool so the job on the 15th won't append to the existing tape.
Hope that helps.